Date/heure
25 mars 2025
10:45 - 11:45
Lieu
Salle de conférences Nancy
Oratrice ou orateur
Lucas Coeuret (Université de Padova)
Catégorie d'évènement
Séminaire Équations aux Derivées Partielles et Applications (Nancy)
Résumé
Le séminaire aura lieu en visio-conférence dans la salle de conférence.
This talk deals with the stability analysis of discrete shock profiles
for systems of conservation laws. These profiles correspond to
approximations of shocks of systems of conservation laws by
conservative finite difference schemes. Discontinuous solutions
appear naturally in the study of systems of conservation laws, which
can model many physical situations, such as gas dynamics. Existence
and stability of discrete shock profiles for each stable shock of the
approximated system of conservation laws is seen as an
improved consistency condition and implies that the finite difference
scheme should be able to approach discontinuities fairly precisely.
The aim of the talk is to review some stability results regarding
discrete shock profiles and to present a recent effort to extend them.
More precisely, most results known up until recently are focused on
the stability of discrete shock profiles associated with shocks
of small amplitude. The talk will focus on a nonlinear orbital
stability result for discrete shock profiles in quite a general
setting, where the smallness assumption on the shock’s amplitude is
replaced by a spectral stability assumption on the linear operator
obtained by linearizing the numerical scheme about the discrete shock
profile. This nonlinear orbital stability result relies on a precise
description of the Green’s function of the linearization about
discrete profiles.